SAT Math Multiple Choice Question 558: Answer and Explanation

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Question: 558

3. Which of the following quadratic equations has no solution?

  • A. 0 = -3(x + 1)(x – 8)
  • B. 0 = 3(x + 1)(x – 8)
  • C. 0 = -3(x + 1)2 + 8
  • D. 0 = 3(x + 1)2 + 8

Correct Answer: D

Explanation:

D

Difficulty: Medium

Category: Passport to Advanced Math / Quadratics

Strategic Advice: Making connections between equations and their graphs will save valuable time on this question. The graph of every quadratic equation is a parabola, which may or may not cross the x-axis, depending on where its vertex is and which way it opens. Don't forget—if the equation is written in vertex form, y = a(x – h)2 + k, then the vertex is (h, k) and the value of a tells you which way the parabola opens.

Getting to the Answer: When an equation has no solution, its graph does not cross the x-axis, so try to envision the graph of each of the answer choices (or you could graph each one in your graphing calculator, but this will probably take longer). When a quadratic equation is written in factored form, the factors tell you the x-intercepts, which means A and B (which are factored) must cross the x-axis, so eliminate them. Now, imagine the graph of the equation in C: The vertex is (–1, 8) and a is negative, so the parabola opens downward and consequently must cross the x-axis. This means (D) must be correct. The vertex is also (–1, 8), but a is positive, so the graph opens up and does not cross the x-axis.

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